Statistics Homework 10.3
Statcrunch solution: For Test Statistic T0 Go to stat--T-Stat-One Sample Data Summary. Sample mean put 8.37 Sample std. dev. put 0..7 Sample size put 12 H0: m= 9.02 HA:m> 9.02 Compute: T0=-3.22 Statcrunch solution for P-value: Go to stat-calculators-T calculator. DF=12 P(X<-3.22 Calculate P value is 0.004 What conclusion can be drawn? Reject H0: There is sufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm3
#3 Question open picture
Open statcrunch. Go to Sample T summary. Sample mean=98.3, Sample std. dev=1.1, Sample size=225 h0: Mu=98.6 HA: Mu<98.6 Compute: t0= 4.09 P-value=0.000 What can be concluded? Reject H0 since the P-value is less than the significance level.
Question #9. Open picture
#1 Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.4 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.02 Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an alpha=0.10 level of significance.
For answers for a) and b) open picture d) (c) Write a conclusion for this hypothesis test assuming a=0.10 level of significance. Reject the null hypothesis. There is sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today
#4 A health administration recommends that individuals consume 950 mg of calcium daily. After an advertising campaign aimed at male teenagers, a dairy association states that male teenagers consume more than the recommended daily amount of calcium. To support this statement, the association obtained a random sample of 40 male teenagers and found that the mean amount of calcium consumed was 960mg, with a standard deviation of 100 mg. Is there significant evidence to support the statement of the association at the alpha equals 0.05 level of significance?
For statcrunch solution open picture What conclusion can be drawn? Do not reject H0. There is not sufficient evidence to conclude that male teenagers consume more than the daily amount of calcium.
#7 Real estate taxes are used to fund local education institutions, police protection, libraries, and other local public services. A household's real estate tax bill is based on the value of the house. In a recent year, the mean real estate tax bill per $1,000 assessed value for all households in a certain country was $7.53. A random sample of 50 rural households results in a sample mean real estate bill per $1,000 assessed value of $6.18 with a standard deviation of $5.90 . Use the level of significance a=0.05. Complete parts (a) and (b).
Statcrunch solution: Go to One Sample T-Summary. Sample mean 6.18, Sample std dev. 5.90, Sample size 50 compute. T-Stat=-1.618 or -1.7 rounded to 2 decimal points For P value we go then go to T-calculator put in DF: 49 P(x<-1.68 compute: P-value =0.112 use the level of significance a=0.05. What can be concluded from the hypothesis test? The evidencenbsp does not suggest nothing that rural households have a different mean real estate tax bill
#2 A college entrance exam company determined that a score of 20 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 200 students who completed this core set of courses results in a mean math score of 20.6 on the college entrance exam with a standard deviation of 3.6. . Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 20 on the math portion of the exam? Complete parts a through d below.
Statcrunch solution: Go to stat--T-Stat-One Sample Data Summary. Sample mean put 20.6 Sample std. dev. put 3.6 Sample size put 200 H0: m= 20 HA:m> 20 b) Verify that the requirements to perform the test using the t-distribution are satisfied. Is the sample obtained using simple random sampling or from a randomized experiment? Yes because the students were randomly sampled. Is the population from which the sample is drawn normally distributed or is the sample size, n, large (n> or =30) Yes, the sample size is larger than 30. Are the sample values independent of each other? Yes, because each student's test score does not affect the other student's test scores. c) P-value =0.009 from your statcrunch State the conclusion for the test. Reject the null hypothesis because the P-value is less than the a=0.10 level of significance.
#8A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with mu =523. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of the 1800 students is 528 with a standard deviation of 111 Complete parts (a) through (d) below.
b. Statcrunch go to One Sample T summary. Sample mean: 528 Sample std. dev.: 111 Sample size 1800 H0: m=523 HA: m>523 calculate t0=1.91 P-Value=0.028 (c) s the sample mean statistically significantly higher? Yes (d) Test the hypothesis at the a=0.10 level of significance with nequals 350 students. Assume that the sample mean is still 528 and the sample standard deviation is still 111. . Is a sample mean of 528 significantly more than 523? Conduct a hypothesis test using the P-value approach. Find the test statistic. T0=0.84 The P-value=0.200 Is the sample mean significantly higher? No What do you conclude about the impact of large samples on the P-value? As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. Statcrunch go to One Sample T summary. P-value=0.483 Write a conclusion for the test. Choose the correct answer below Do not reject the null hypothesis. There is not sufficient evidence to conclude the mean IQ score of people in the country is greater than 103.
#5 The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table. Complete parts
For statcrunch solution: open table in statcrunch. Go to stats-T stats-one sample-data. Look under T-stat on the table. T0=-1.22 We then go to T-calculator put in 10 of DF. P(x<-1.22 compute: P-value is 0.125 The P-value is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective.
#6A golf association requires that golf balls have a diameter that is 1.68 inches. To determine if golf balls conform to the standards, a random sample of golf balls was selected. Their diameters are shown in the table. Complete parts (a) and (b).
Statcrunch solution: Go to stats-T stats-one sample-data. Select column under Diameter. Select Ho m=1.68, Ha: m does not equal 1.68 compute: T-stat T0=0.81 P-value 0.436 There is not sufficient evidence to conclude that the golf balls do not conform to the association's standards.
