Exam 8: Hypothesis Testing

Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29 with a standard deviation of five hours. A sample of 49 people had an average of 31 hours that they could go without sleep and still function normally. The test value for this hypothesis would be 2.8.

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean $\mu$ . Do you reject $H _ { 0 }$ at the $\alpha = 0.10$ level of significance?

A recent survey of gasoline prices indicated that the national average was $\$ 4.098$ per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $\$ 3.924$ per gallon with a population standard deviation of $\$ 0.053$ . What critical value should be used to test the claim using $\alpha = 0.01$ ?

It has been claimed that at UCLA at least $40 \%$ of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at $\alpha = 0.01$ ?

A sample of 46 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE). The participants take a mc GRE test before the program begins and again at the end to measure their improvement. The mean number of points improved was $\bar { x } = 16$ . Assume the standard deviation is $\sigma = 53$ and let $\mu$ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ . ive Compute the value of the test statistic.

In a simple random sample of size 88 , there were 22 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.31$ versus $H _ { 1 } : p < 0.31$ . Compute the test statistic $z$

The mean annual tuition and fees for a sample of 11 private colleges was $26,500 with a standard deviation of $6000. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $31,000. i). State the null and alternate hypotheses. ii). Compute the value of the test statistic and state the number of degrees of freed iii). State a conclusion regarding $H _ { 0 }$ . Use the $\alpha = 0.05$ level of significance. .

A test is made of $H _ { 0 } : \mu = 60$ versus $H _ { 1 } : \mu > 60$ . A sample of size $n = 77$ is drawn, and $\bar { x } = 64$ . The population standard deviation is $\sigma = 23$ . Compute the value of the test statistic $z$ and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.05$ level.

Which type of null hypothesis is used in the figure below?

A test of $H _ { 0 } : \mu = 49$ versus $H _ { 1 } : \mu < 49$ is performed using a significance level of $\alpha = 0.05$ . The value of the test statistic is $z = - 1.70$ . If the true value of $\mu$ is 45 does the conclusion result in a Type I error, a Type II error, or ह correct decision?

The following display from a TI-84 Plus calculator presents the results of a hypothesis tes What are the null and alternate hypotheses?

Thirty-seven members of a bowling league sign up for a program that claims to in bowling scores. The participants bowl a set of five games before the program begi a set of five games again at the end to measure their improvement. The mean number of points improved (over the set of five games) was $\bar { x } = 22$ . Ass the standard deviation is $\sigma = 44$ and let $\mu$ be the population mean number of points improved for the set of five games. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ . i). Compute the value of the test statistic. ii). Compute the $P$ -value. iii). Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level? ove

Nationwide, the average waiting time until a electric utility customer service representative answers a call is 310 seconds. The Gigantic Kilowatt Energy Company Randomly sampled 40 calls and found that, on average, they were answered in 287 Seconds with a population standard deviation of 30 seconds. Can the company claim that They are faster than the average utility at α = 0.05?

The Energy Information Administration reported that $51.5 \%$ of homes in the United States were heated by natural gas. A random sample of 200 homes found that 111 heated by natural gas. Does the evidence support the claim or has the percentage changed? Use $\alpha = 0.05$ and the $P$ -value method.

A test of $H _ { 0 } : \mu = 65$ versus $H _ { 1 } : \mu < 65$ is performed using a significance level of $\alpha = 0.05$ . The $P$ -value is $0.055$ . If the true value of $\mu$ is 65 , does the conclusion result in a Type I error, a Type II error, or correct decision?

The average greyhound can reach a top speed of $18.8$ meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 50 of her dogs ran, on average, $19.2$ meters per second with a population standard deviation of $1.4$ meters per second. With $\alpha = 0.05$ , is her claim correct?

Assume that a $95 \%$ confidence interval for the mean is $15.0 < \mu < 17.0$ . The null hypothesis $H _ { 0 } : \mu = 14.0$ at $\alpha = 0.05$ would

The following output from MINITAB presents the results of a hypothesis test for a population mean $\mu$ . Test of $\mathrm { mu } = 46 \mathrm { vs } .$ not $= 46$ Mean StDev SE Mean 95\% CI P 65 43.40 7.941089 0.984971 (41.432298,45.367702) -2.639672 0.0104 What is the value of $\bar { x }$ ?