Hypothesis Testing (Advanced Algebra)
A company claims that its tablet computers have an average recharge time of 3 hours with a standard deviation of 1.4 hours. Using a random sample of 50 company tablet computers, a consumer group determines a mean recharge time of 2.5 hours. H0: µ = 3 Ha: µ < 3 a = 5% σ = 1.4 z* = -1.65 Using this formula, calculate the value of the z-statistic. Round your answer to the tenths place.
-2.5
Brett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20. His sample data has a mean of 295 and a sample size of 50. Which of the following correctly depicts the z-statistic for Brett's data?
-5.30
The owners of an eyeglass store claim that they fill customers' orders, on average, in 60 minutes with a standard deviation of 15.9 minutes. Based on a random sample of 40 orders, a reporter determines a mean order time of 63 minutes. Let µ represent the average number of minutes to fill an order. To the nearest hundredth, the z-statistic isz =
1.19
A company claims that its tablet computers have an average recharge time of 3 hours. Using a random sample of 50 company tablet computers, a consumer group determines a mean recharge time of 2.5 hours with a standard deviation of 0.3 hours. H0: µ = 3 Ha: µ < 3 a = 5% z^x = -
1.65
The reporter wants to test the store's claim against the alternative hypothesis that the wait time is actually greater than 60 minutes. What is the critical value for z for a hypothesis test using a 5% significance level?z* =
1.65
Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. His sample size is 7 with a mean of 93.5. Which of the following correctly depicts the z-statistic for this data?
1.98
In a normal population, 95% of the values lie within how many standard deviations of the mean?
2
A company claims that its packages of beads contain, on average, 50 beads with a standard deviation of 5.4 beads. In a hypothesis test of this claim, H0 is µ = 50 and Ha is µ ≠ 50, where µ is the average number of beads per package. Based on a sample of 20 packages, Celia calculates a mean of 52.5 beads per package. Formula for z-statistic: What is the z-statistic for the sample? Round the answer to the nearest hundredth.z =
2.07
A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298.4 mL. Using the given table, which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL?
2.5%
A company advertises that there are an average of 25 grams of potato chips in each bag of chips. A consumer group has collected a sample and wants to perform a test to see if the company is providing less than it advertises. H0: μ = 25 Ha: μ < 25 Which type of significance test should be used for this situation?
A left tailed test
Julian is a manager at a clothing store for teens. He is analyzing the order for next season. Data for the previous 10 years suggests that teens are willing to spend an average of $75 for a pair of designer jeans with a standard deviation of $5. However, Julian thinks the average may have changed due to a recession. He finds that the last three seasons of data show that teens spent an average of $68 on a pair of jeans. Therefore, he performed a hypothesis test to see if the recent average is the same. Julian used a significance level of 5% to perform the test. Which of the following statements is valid based on the results?
Julian's data shows that the recent seasons' average jean price is not $75.
Tyesha found that the z-statistic was 2.1 and that the critical z-values were -1.96 and 1.96. Which of the following is a valid conclusion based on these results?
One can reject the null hypothesis.
Based on the hypothesis test, what conclusion can you draw about the statistical claim that the average recharge time of the tablet computers is 3 hours?
The claim should be rejected
A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. On average, when surveyed regarding job satisfaction, teachers give a score of 3.3 out of 5 with a standard deviation of 0.6. When the authors of the study interviewed 40 teachers who supplemented with their own materials, they found 3.5 to be the mean. The authors wanted to know if the group of teachers that could choose supplementary curriculum had a higher level of job satisfaction. They used a significance level of 1%. Which of the following statements is valid based on the results of the test?
The data shows that the authors cannot make a determination either way with this data.
The critical value for z* for a hypothesis test of the claim at 5% significance is z* = 1.96. How should the z-statistic for the sample be interpreted in terms of the hypothesis test?
The null hypothesis should be rejected.
A hypothesis test has a significance level of 10%. Explain what this significance level represents.
The significance level determines the critical region of the hypothesis test. A significance level of 10% means that there is a 10% probability of rejecting the null hypothesis incorrectly.
A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?
The z-statistic is 3.32, so the null hypothesis should be rejected.
Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting the null hypothesis?
The z-statistic lies in the critical region.
Based on the hypothesis test, what conclusion can be drawn about Delmar's claim?
There is not enough evidence to accept or reject his claim.
Delmar claims that, on average, he practices the piano at least 2 hours per day. In a hypothesis test of this claim, H0 is µ ≥ 2 and Ha is µ < 2, where µ is the number of hours, on average, Delmar practices daily. The diagram shows the critical region for the hypothesis test. The z-statistic for a sample of Delmar's practice times is 1.41. How should this statistic be interpreted in terms of the hypothesis test? should be rejected. should be accepted. There is not enough evidence to reject .
There is not enough evidence to reject H0
Based on the z-statistic of -2.5 for the sample data, should the null hypothesis be rejected? Yes, because the z-statistic lies within the critical region. Yes, because the z-statistic lies outside of the critical region. No, because the z-statistic lies within the critical region. No, because the z-statistic lies outside of the critical region. Hypothesis Test for Tablet Recharge Time H0: µ = 3 Ha: µ < 3 a = 5% z= -2.5
Yes, because the z-statistic lies within the critical region.
You have reason to believe that there are actually fewer raisins in each box than the company claims. Your alternative hypothesis, , would be
a
The speed limit on a road is 45 mph. You want to clock the speed of a random sample of cars to test the hypothesis that the average speed of cars is greater than the speed limit. What kind of test would you use?
a right tailed test
What type of significance test should be used for this situation?
a right tailed test
The ____________ hypothesis represents the statistical claim that the company's tablet computers have an average recharge time of less than 3 hours.
alternative
A basketball coach claims that the team's players commit, on average, no more than 10 fouls per game. Let µ represent the team's average number of fouls per game. Another coach thinks that these players create more fouls. What is the null hypothesis, H0, for this situation?
b
A company claims that its tablet computers have an average recharge time of 3 hours. In a random sample of these computers, the average recharge time is 2.5 hours. You suspect that the average recharge time might be less than what the company claims. Let µ represent the average time, in hours, needed to recharge the company's tablet computers. What is the null hypothesis, , for this situation?
b
A meteorologist claims that the average daily high temperature in Oklahoma City is 90°F. Let µ represent the average daily high temperature, in °F, in Oklahoma City during the summer. What is the null hypothesis, H0, for this situation?
b
What is the alternative hypothesis, Ha, for this situation?
b
What is the alternative hypothesis,, for this situation?
b
You have reason to believe that there are actually more raisins in each box than the company claims. Your alternative hypothesis, , would be
b
You have sample data that leads you to believe that the average high temperature in Oklahoma City is 92°F. What is the alternative hypothesis, Ha, for this situation?
b
A cereal manufacturer claims that there are an average of 200 raisins in each box of cereal. Let µ represent the average number of raisins per box of cereal. You want to test this claim. What is the null hypothesis, , for this situation?
d
The mean and the standard deviation of a normal population are called ____________. The mean and the standard deviation of a random sample from a population are called _____________.
parameters statistics
