MCQs & Hypothesis Testing Problems

Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (u,p, σ) for the indicated parameter.

1) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, u, of 46 degrees F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

A)H0: u=46 degrees
H1: u=46 degrees

B)H0: u=46 degrees
H1:u ≠ 46 degrees

C)H0: u ≤ 46 degrees
H1: u>46 degrees

D)H0:u ≥ 46 degrees
H1:u<46 degrees

2) Find the critical z value(s). Assume that the data has a normal distribution
&#913; = 0.05 for a two-tailed test
A)Plus or minus 1.96
B)Plus or minus 1.764
C)Plus or minus 1.645
D)Plus or minus 2.575

3) &#963; = 0.05 for a left-tailed test.
A)Plus or minus 1.96
B)-1.96
C)-1.645
D)Plus or minus 1.645

4) Find the value of the test statistic z using z=p-p/&#8730;pq/n
The claim is that the proportion of drowning deaths of children attribute to beaches is more than 0.25, and the sample statistics include n=603 drowning deaths of children with 30% of them attributable to beaches.

A)-2.68
B)2.84
C) 2.68
D) -2.84

5) Use the given information to find the P-value.
The test statistic in a left-tailed test z = -1.83
A)0.0336
B)0.0443
C)0.4326
D)0.4232

6) Formulate the indicated conclusion in nontechinical terms Be sure to address the original claim.

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz.

B)There is sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz.

C)There is not sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz.

D)There is not sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz.

7) Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, u of 41 degrees F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Identify the type I error for the test

A)The error of rejecting the claim that the mean temperature equals 41 degrees F when it is really different from 41 degrees F.

B)The error of rejecting the claim that the mean temperature equals 41 degrees F when it really does equal 41 degrees F.

C)The error of failing to reject the claim that the mean temperature equals 41 degrees F when it is really different from 41 degrees F.

8. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.

Test the claim that for the population of female college students, the mean weight is given by u = 132 lb. Sample data are summarized as n=20, x = 137 lb, and s = 14.2 Use a significance level of &#963;= 0.1

9. Find the number of successes x suggested by the given statement.
Among 770 people selected randomly from among the residents of one city, 17.14% were found to be living below the official poverty line.

A)136
B)128
C)137
D)132

10. From the sample statistics, find the value of p used to test the hypothesis that the population proportions are equal. N1=392 N2=151 X1= 73 X2=98

A) 0.157
B) 0.315
C) 0.283
D) 0.220

11. Compute the test statistic used to test the null hypothesis that P1=P2.
N1 = 168 n2=161 x1=72 x2 = 67

A)5.412
B)0.432
C)2.914
D)0.227

12. Find the appropriate null hypothesis, H0: P1=P2, using a significance level of 0.05.
N1=200 n2 = 100 x1 = 11 x2 = 8

A).0201
B).0012
C).1011
D).4010

13. Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected.

Use the given sample data to test the claim that P1>P2. Use a significance level of 0.01.
Sample 1: n1=85 x1=38
Sample 2: n2=90 x2 = 23

14. Construct the indicated confidence interval for the difference between population proportions P1-P2. Assume that the samples are independent and that they have been randomly selected.
X1=34, n1=70 and x2=44, n2=74; Construct a 95% confidence interval for the difference between population proportions P1-P2.

A)0.293<P1-P2<0.678
B)-0.271<P1-P2<0.053
C)0.324<P1-P2<0.648
D)-0.301<P1-P2<0.678

Determine whether the samples are independent or consistent of matched pairs.
The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group who use placebo drug

A)Matched pairs
B)Independent samples

15. Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected.

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data to test the claim that the treatment population mean u1 is smaller than the control population mean u2. Test the claim using a significance level of 0.01.

Treatment Group: n1=85 x1=189.1 s1=38.7
Control Group
N2=75
X2=203.7
S2=39.2

16. Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 99% confidence interval for u1-u2 where u1 and u2 represent the mean for the treatment group and the control group respectively.

Treatment group: n1=85 x1=189.1 s1=38.7
Control Group: N2=75 x2=203.7 s2 = 39.2
A)-26.7<u1-u2<-2.5
B)-29.0<u1-u2<-0.2
C)-30.5<u1-u2<1.3
D)-1.3<u1-u2<30.5

17. The two data sets are dependent. Find the d to the nearest tenth.
X|60 54 63 63 51
Y|23 23 30 25 22

A)33.6
B)43.7
C)42.0
D)20.2

18. Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is ud=0. Compute the value of the t test statistic.
X|8 6 7 2 8
Y|5 8 3 3 3

A)T=2.890
B)T=0.578
C)T=0.415
D)T=1.292

19.Construct a confidence interval for ud, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
If d=3.125, Sd=2.911, and n=8, determine a 90 percent confidence interval for ud.

A)2.435<ud<3.815
B)1.175<ud<5.075
C)2.435<ud<5.075
D)None of the above is correct

20. Find the odds ratio:
Disease | No disease
Treatment: 57 88
Placebo: 33 117
A)2.2965
B)0.1827
C)0.4354
D)1.2991

21. Construct a 95% confidence interval estimate of the odds ratio

Disease | No Disease

Treatment 55 83

Placebo 45 95

A)O.6530 OR 1.7463
B)0.8554 OR 2.2878
C)0.4371 OR 1.1690
D)0.1919 OR 0.5133

22. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher's claim at the 0.05 significance level.

23. The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that &#963; is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weighs less than 200 lb.