Statistic
The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant's eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 9 days following no advertisements, the mean was 21.8 purchasing customers with a standard deviation of 1.5 customers. On 11 days following advertising, the mean was 23.1 purchasing customers with a standard deviation of 1.9 customers. Test the claim, at the 0.10 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 40 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.560. Determine if there is sufficient evidence to say that his batting average has improved at the 0.02 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 44 at bats. For a random sample of 80 at bats since changing his training techniques, his batting average is 0.475. Determine if there is sufficient evidence to say that his batting average has improved at the 0.05level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 7 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $16. For 12 randomly selected customers of Company B, you find that they pay a mean of $160 per month with a standard deviation of $14. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.10 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 38 participants in the treatment group lowered their cholesterol levels by a mean of 22.5 points with a standard deviation of 1.3 points. The 31 participants in the control group lowered their cholesterol levels by a mean of 21.1 points with a standard deviation of 2.9 points. Assume that the population variances are not equal and test the company's claim at the 0.02 level. Let the treatment group be Population 1 and let the control group be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. -The number of cigarettes a person smokes per day and their life expectancy -The retail price of a particular style of jeans and the number of units sold at that price -The number of crimes committed in an area and the selling price of homes in that area -A person's age and the clarity of their vision -The retail price of a particular tablet and the number of units sold at that price -A child's age and the number of hours spent napping -
Negative
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. -The average cost of a laptop and the attendance at a water park on a given day -The gross earnings of a movie and the number of jackets sold on a given day -The number of video games sold and the cost of a loaf of bread on a given day -the number of pets owned by a family and the value of their house -The number of bikes manufactured and the amount of cheese consumed on a given day -your daily calorie intake and your GPA -the age of a car and the owner's age -The temperature and the selling price of homes -the number of times a person exercises per week and the amount of time they spend on the phone
No correlation
Step 2 of 3 : Determine if r is statistically significant at the 0.01 level.
No, the correlation coefficient is not statistically significant
Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.2500.250 in a random sample of 4444 at bats. For a random sample of 8080 at bats since changing his training techniques, his batting average is 0.4750.475. Determine if there is sufficient evidence to say that his batting average has improved at the 0.050.05 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2. Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.050.05 level of significance to say that Adrian's batting average has improved since he changed his training methods.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.050.05 level of significance to say that the mean exam scores for the two classes are different.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.050.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.050.05 level of significance to support the claim that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.050.05 level of significance to support the company's claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.100.10 level of significance to support the claim that customers of Company A pay less for car insurance, on average, than customers of Company B.
Step 2 of 3 : Determine if r is statistically significant at the 0.050.05 level.
Yes, the correlation coefficient is statistically significant
For the given scenario, determine the type of error that was made, if any. (Hint: Begin by determining the null and alternative hypotheses.) The mathematics department at one university reports 30% as the failure rate for College Algebra. One student claims that the failure rate for College Algebra is less than 30%. The student conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the failure rate for College Algebra is 26%. Was an error made? If so, what type?
Yes; Type II error
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 28 35 37 43 49 Number of Bids 3 4 5 7 8 Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer look at a and that should be the slope
Step 2 of 6 : Find the estimated y-intercept. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer look at b and that should be the y-intercept
The following table compares the completion percentage and interception percentage of 55 NFL quarterbacks. Completion Percentage 55.5 57.5 58.5 59 59.5 Interception Percentage 5 4.5 4 3 1.5 Determine if r is statistically significant at the 0.01 level.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer for r and then go to the table and click Pearson correlation coefficient. Since we have 5 value so look for five and 0.01 since 0.01 for 5 is 0.959 and our r is 0.855, since it less than 0.959 the answer will be No.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 180 engines and the mean pressure was 7.5 pounds/square inch (psi). Assume the population standard deviation is 0.9. If the valve was designed to produce a mean pressure of 7.7 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?
p=0.0029 Comparing the P-value we calculated to the level of significance, we see that 0.0029≤0.05, so we will make the decision to reject the null hypothesis. We can interpret this decision in terms of the original claim to mean that there is sufficient evidence to support the claim that the valve does not perform to the specifications. ->There is sufficient evidence to support the claim that the valve does not perform to the specifications.
A psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.02 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below
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A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 200 randomly selected people who rode a jet ski, 87% wore life vests. Out of 500 randomly selected boaters, 93.2% wore life vests. Using a 0.05 level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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An economist studying inflation in electricity prices in 2018 and 2019 believes that the average price of electricity, even after adjusting for inflation, changed between these two years. To test his claim, he samples 9 different counties and records the average price of electricity in each county from each year. He then adjusts the prices for inflation. His results are given in the following table. Test the economist's claim at the 0.10 level of significance assuming that the population distribution of the paired differences is approximately normal. Let prices in 2018 be Population 1 and prices in 2019 be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below
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To test the fairness of law enforcement in its area, a local citizens' group wants to know whether women and men are unequally likely to get speeding tickets. Three hundred randomly selected adults were phoned and asked whether or not they had been cited for speeding in the last year. Using the results in the following table and a 0.020.02 level of significance, test the claim of the citizens' group. Let men be Population 1 and let women be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class 1, the mean exam score for 18 students is 81.4 with a standard deviation of 5.6. In Class 2, the mean exam score for 16 students is 76.3 with a standard deviation of 6.6. Test the professor's claim at the 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are equal. Let Class 1 be Population 1 and let Class 2 be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
≠ H0: μ1=μ2. Ha: μ1≠μ2
A newsletter publisher believes that less than 46% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
There is sufficient evidence at the 0.05 level of significance that the percentage is less than 46%
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
200(0.87)=x1 500*0.932=x2 STAT->Test->6 look at the z for answer
A sample of 1300 computer chips revealed that 76% of the chips do not fail in the first 10001000 hours of their use. The company's promotional literature claimed that more than 73% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.10 level to support the company's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.73 Ha: p>0.73
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
Stat->Edit->put in the data and l3 put in the difference->STAT->TEST->T-Test u is 0 =-2.936
A newsletter publisher believes that more than 72% of their readers own a personal computer. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.72 Ha: p>0.72
To test the fairness of law enforcement in its area, a local citizens' group wants to know whether women and men are unequally likely to get speeding tickets. Four hundred randomly selected adults were phoned and asked whether or not they had been cited for speeding in the last year. Using the results in the following table and a 0.010.01 level of significance, test the claim of the citizens' group. Let men be Population 1 and let women be Population 2. Step 3 of 3 : Draw a conclusion and interpret the decision.
We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.010.01 level of significance to support the local group's claim that women and men are unequally likely to get speeding tickets.
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
|t|>1.721
To test the fairness of law enforcement in its area, a local citizens' group wants to know whether women and men are unequally likely to get speeding tickets. Four hundred randomly selected adults were phoned and asked whether or not they had been cited for speeding in the last year. Using the results in the following table and a 0.010.01 level of significance, test the claim of the citizens' group. Let men be Population 1 and let women be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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A sample of 1200 computer chips revealed that 47% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that less than 50% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.10 level to support the company's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.5 Ha: p<0.5
A newsletter publisher believes that less than 55% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.55 Ha: p<0.55
A newsletter publisher believes that 57% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.10 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.57 Ha: p≠0.57
Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.8 hours with a standard deviation of 0.2 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.4 hours to paint each room with a standard deviation of 0.3 hours. At the 0.05 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 5.8 pounds/square inch (psi). Assume the population standard deviation is 1.0. The engineer designed the valve such that it would produce a mean pressure of 6.0 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Make the decision to reject or fail to reject the null hypothesis.
Comparing the P-value we calculated to the level of significance, we see that 0.0047≤0.02, so we will make the decision to reject the null hypothesis. ->Reject Null Hypothesis
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 270 engines and the mean pressure was 5.6 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 5.5 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?
Comparing the P-value we calculated to the level of significance, we see that 0.0404>0.02, so we fail to reject the null hypothesis. We can interpret this decision in terms of the original claim to mean that there is not sufficient evidence to support the claim that the valve does not perform to the specifications. ->There is not sufficient evidence to support the claim that the valve does not perform to the specifications.
An automobile manufacturer has given its jeep a 56.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 160 jeeps, they found a mean MPG of 56.4. Assume the population variance is known to be 4.41. Is there sufficient evidence at the 0.05 level to support the testing firm's claim?
Comparing the P-value we calculated to the level of significance, we see that 0.0703>0.05, so we fail to reject the null hypothesis. We can interpret this decision in terms of the original claim to mean that there is not sufficient evidence to support the claim that the jeeps have an incorrect manufacturer's MPG rating. ->There is not sufficient evidence to support the claim that the jeeps have an incorrect manufacturer's MPG rating
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 437 gram setting. It is believed that the machine is underfilling the bags. A 35 bag sample had a mean of 434 grams. Assume the population standard deviation is known to be 14. Is there sufficient evidence at the 0.02 level that the bags are underfilled?
Comparing the P-value we calculated to the level of significance, we see that 0.1020>0.02, so we fail to reject the null hypothesis. We can interpret this decision in terms of the original claim to mean that there is not sufficient evidence to support the claim that the bags are underfilled. ->There is not sufficient evidence to support the claim that the bags are underfilled
Step 3 of 3 : Make the decision to reject or fail to reject the null hypothesis.
Comparing the P-value we calculated to the level of significance, α, we see that 0.0052≤0.05, so we will make the decision to reject the null hypothesis ->Reject Null Hypothesis
Step 3 of 3:
Comparing the P-value we calculated to the level of significance, α, we see that 0.1056>0.02, so we fail to reject the null hypothesis. Fail to Reject Null Hypothesis
A sample of 1500 computer chips revealed that 27% of the chips fail in the first 10001000 hours of their use. The company's promotional literature claimed that 30% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.
H0: p=0.3 Ha: p≠0.3
A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 15 bottles of regular cola has a mean of 500.8mLL of soda with a standard deviation of 2.2mL. A random sample of 1818 bottles of diet cola has a mean of 498.3mL of soda with a standard deviation of 3.6mL. Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.01 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
H0: μ1=μ Ha:μ1≠μ2
The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 318 minutes. For a sample of 80 patients, the mean time the drug stayed in the system was 324 minutes. Assume the population standard deviation is 21. Step 1 of 3 : State the null and alternative hypotheses.
H0: μ=318 Ha: μ>318
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 408 grams with a standard deviation of 14. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
H0: μ=410 Ha: μ<410
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 417 gram setting. It is believed that the machine is overfilling the bags. A 34 bag sample had a mean of 423 grams. Assume the population standard deviation is known to be 28. Is there sufficient evidence at the 0.02 level that the bags are overfilled? Step 1 of 3 : State the null and alternative hypotheses.
H0: μ=417 Ha: μ>417
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 419 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.
H0: μ=419 Ha: μ≠419
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 431 gram setting. Based on a 26 bag sample where the mean is 441 grams and the standard deviation is 20, is there sufficient evidence at the 0.01 level that the bags are overfilled? Assume the population distribution is approximately normal. State the null and alternative hypotheses.
H0: μ=431 Ha: μ>431
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 440 gram setting. Is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.
H0: μ=440 Ha: μ>440
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 445 gram setting. Is there sufficient evidence at the 0.1 level that the bags are underfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.
H0: μ=445 Ha: μ<445
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240 engines and the mean pressure was 55 lbs/square inch. Assume the standard deviation is known to be 0.7. If the valve was designed to produce a mean pressure of 5.1 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs BELOW the specifications? State the null and alternative hypotheses for the above scenario.
H0: μ=5.1 Ha: μ<5.1 BELOW
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 230 engines and the mean pressure was 6.3 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 6.2 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs ABOVE the specifications? State the null and alternative hypotheses for the above scenario.
H0: μ=6.2 Ha: μ>6.2 ABOVE
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.8 lbs/square inch. Assume the standard deviation is known to be 0.9. If the valve was designed to produce a mean pressure of 6.7 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.
H0: μ=6.7 Ha: μ≠6.7
Using traditional methods, it takes 9.0 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 17 students and observed that they had a mean of 9.2 hours with a standard deviation of 1.1. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
H0: μ=9 Ha: μ≠9
For the given scenario, determine the type of error that was made, if any. (Hint: Begin by determining the null and alternative hypotheses.) ->A radio station has accepted 26 as the mean age of its listeners. One radio station executive claims that the mean age of its listeners is less than 26. The radio station executive conducts a hypothesis test and rejects the null hypothesis. Assume that in reality, the mean age of its listeners is 24. Was an error made? If so, what type? ->A new whitening toothpaste advertises four shades as the mean number of shades the toothpaste whitens your teeth. One user claims that the mean number of shades the toothpaste whitens your teeth is different from four shades. The user conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean number of shades the toothpaste whitens your teeth is four shades. Was an error made? If so, what type? ->Economists considered $3.110$3.110 as the mean price for gallon of unleaded gasoline in the United States in a certain year. One consumer claims that the mean price for gallon of unleaded gasoline in the United States in a certain year is different from $3.110$3.110. The consumer conducts a hypothesis test and rejects the null hypothesis. Assume that in reality, the mean price for gallon of unleaded gasoline in the United States in a certain year is $3.210$3.210. Was an error made? If so, what type? A cell phone company claims only $50$50 as the mean amount its customers spend on cell phone service per month. One passionate salesperson claims that the mean amount its customers spend on cell phone service per month is less than $50$50. The passionate salesperson conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean amount its customers spend on cell phone service per month is $50$50. Was an error made? If so, what type? ->An ice cream truck aims to keep 3030 degrees as the mean temperature inside its delivery truck. One employee claims that the mean temperature inside its delivery truck is more than 3030 degrees. The employee conducts a hypothesis test and rejects the null hypothesis. Assume that in reality, the mean temperature inside its delivery truck is 3232 degrees. Was an error made? If so, what type? ->Researchers state 2.52.5 hours as the mean amount of television watched by children per night. One parent claims that the mean amount of television watched by children per night is less than 2.52.5 hours. The parent conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean amount of television watched by children per night is 2.52.5 hours. Was an error made? If so, what type? ->A pharmaceutical company claims only 2%2% as the percentage of people taking a particular drug that experience significant side effects. One researcher claims that the percentage of people taking a particular drug that experience significant side effects is less than 2%2%. The researcher conducts a hypothesis test and rejects the null hypothesis. Assume that in reality, the percentage of people taking a particular drug that experience significant side effects is 0.5%0.5%. Was an error made? If so, what type? -->A travel agency states $700$700 as the mean cost per person of their four-day vacation packages. One travel agent claims that the mean cost per person of their four-day vacation packages is less than $700$700. The travel agent conducts a hypothesis test and rejects the null hypothesis. Assume that in reality, the mean cost per person of their four-day vacation packages is $655$655. Was an error made? If so, what type?
No; correct decision
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. -The intensity of exercise and your heart rate -The number of hours you spend studying for a test and your grade on the test
Positive
. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
STAT->TEST->2-SampTTest -1.427
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
STAT->TEST->2-SampTTest 2.438
. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Answer
STAT->TEST->2-SampTTest s=standard deviation x=mean n=sample 2.448
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
STAT->TEST->2-SampTTest −1.668
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
STAT->TEST->2-SampTTest ≈2.816
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 pounds/square inch (psi). Assume the population standard deviation is 0.6. The engineer designed the valve such that it would produce a mean pressure of 4.8 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
STAT->TEST->Z-TEST(1)->STAT look at z answer:1.67
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 425 gram setting. It is believed that the machine is underfilling the bags. A 37 bag sample had a mean of 415 grams. Assume the population variance is known to be 729. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
STAT->TEST->Z-TEST(1)->STAT p=0.122
The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 378 minutes. For a sample of 90 patients, the mean time the drug stayed in the system was 384 minutes. Assume the population standard deviation is 22. Find the P-value of the test statistic.
STAT->TEST->Z-TEST(1)->STAT x is the mean p=0.0048
The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 318 minutes. For a sample of 80 patients, the mean time the drug stayed in the system was 324 minutes. Assume the population standard deviation is 21. Step 2 of 3 : Find the P-value for the hypothesis test. Round your answer to four decimal places.
STAT->TEST->Z-TEST(1)->STAT x=324 u=318 o=21 n=80 answer: 0.0052->0.0053-0.0001
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 417 gram setting. It is believed that the machine is overfilling the bags. A 34 bag sample had a mean of 423 grams. Assume the population standard deviation is known to be 28. Is there sufficient evidence at the 0.02 level that the bags are overfilled? Step 2 of 3 : Find the P-value for the hypothesis test. Round your answer to four decimal places.
STAT->TEST->Z-TEST(1)->STAT x=423 u=417 o=28 n=34 Answer:0.1056->0.1057-0.0001=0.1056
An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to two decimal places.
STAT->TEST->Z-TEST-STAT look Z Answer:-2.50
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
STAT->Test->2-SampTTest 2.491
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 430 gram setting. It is believed that the machine is underfilling the bags. A 17 bag sample had a mean of 423 grams with a variance of 676. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
STAT_>TEST->T-TEST There is not sufficient evidence to support the claim that the bags are underfilled.
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places
Stat->Edit->put in the data and l3 put in the difference->STAT->TEST->T-Test
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
Stat->Edit->put in the data and l3 put in the difference->STAT->TEST->T-Test
Using traditional methods it takes 100 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time
A newsletter publisher believes that 22% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm fails to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
There is not sufficient evidence at the 0.05 level of significance that the percentage is not 22% explaination:
A newsletter publisher believes that less than 44% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser failed to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
There is not sufficient evidence at the 0.05 level of significance to say that the percentage is less than 44%
Using traditional methods it takes 109 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. After performing the test on 130 students, the researcher decides to reject the null hypothesis at a 0.01 level of significance. What is the conclusion?
There is sufficient evidence at the 0.01 level of significance that the new technique lengthens training time.
A newsletter publisher believes that 55% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
There is sufficient evidence at the 0.05 level of significance that the percentage is not 55%
Draw a conclusion and interpret the decision.
We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.01 level of significance to support the claim that the cream reduces the appearance of fine lines and wrinkles after 14 days of application. Back to Practice
A psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.02 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. Step 3 of 3 : Draw a conclusion and interpret the decision.
We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the claim that there is a significant difference between the IQs of spouses.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to say that Adrian's batting average has improved since he changed his training methods.
To test the fairness of law enforcement in its area, a local citizens' group wants to know whether women and men are unequally likely to get speeding tickets. Three hundred randomly selected adults were phoned and asked whether or not they had been cited for speeding in the last year. Using the results in the following table and a 0.020.02 level of significance, test the claim of the citizens' group. Let men be Population 1 and let women be Population 2. Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.020.02 level of significance to support the local group's claim that women and men are unequally likely to get speeding tickets.
Step 3 of 3 : Draw a conclusion and interpret the decision.
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the researcher's claim that the proportion of people who wear life vests is different for jet skiers and boaters.
A lumber company is making boards that are 2932.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 18 boards is made, and it is found that they have a mean of 2933.5 millimeters with a standard deviation of 13.0. Is there evidence at the 0.1 level that the boards are either too long or too short? Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?
df=18−1=17 is 1.740 go to STAT->TEST->T-TEST t=0.490 if it less than -1.740 or more than 1.740 then it is reject so there sufficient evidence. ->There is not sufficient evidence to support the claim that the boards are either too long or too short.
A lumber company is making boards that are 2932.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 18 boards is made, and it is found that they have a mean of 2933.5 millimeters with a standard deviation of 13.0. Is there evidence at the 0.1 level that the boards are either too long or too short? Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?
go to STAT->TEST->T-TEST t=0.490 ta/2 0.1/2=0.05 18-1=17 go to the tabel one-tail-->1.74 if it less than -1.74 or more than 1.74, then it'll be reject. -->There is not sufficient evidence to support the claim that the boards are either too long or too short
The following data gives the number of hours 55 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0 2 3 4 6 Midterm Grades 60 63 69 75 81 Copy Data Calculate the coefficient of determination, r^2. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer
A study of bone density on 55 random women at a hospital produced the following results. Age 37 41 49 53 61 Bone Density 355 335 330 325 310 Step 1 of 3 : Calculate the correlation coefficient, r. Round your answer to six decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer ------>−0.953953
Step 3 of 3 : Calculate the coefficient of determination, r2. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer ---->0.910
The following data gives the number of hours 77 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0.50 .51 .52 3 3.5 4 4.5 Midterm Grades 72 78 81 87 90 96 99 step 1: Calculate the correlation coefficient, r. Round your answer to six decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer ---->0.984180
A study of bone density on 55 random women at a hospital produced the following results. Age 37 49 57 61 69 Bone Density 350 345 335 320 310 Calculate the correlation coefficient, r. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer ---->−0.946
The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0 0.5 1 2 2.5 3 4 4.5 5 5.5 Midterm Grades 60 63 75 81 84 87 90 93 96 99 Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer --->0.970
Calculate the coefficient of determination, r^2. Round your answer to three decimal places.
go to calculator and go to EDIT in STAT and input the x and y in L1 and L2 go to STAT and CAL and press 4 and enter twice to get the answer -->0.969
