The National Weather Service says that the mean daily high temperature for Octob

Question

The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 56 degree F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean. is actually lower than 56 degree F. A simple of mean daily high temperatures for October over past 37 years yields x = 54 degree F. Assume that the population standard deviation is 5.6 degree F. Perform the hypothesis test at the 1% significance level. A manufacturer makes steel bars that are supposed to have a mean length of 50 cm. A retailer suspects that the bars are running too long. A sample of 43 bars is taken and their mean length is determined to be 51 cm. Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is greater than 50 cm. Assume that the population standard deviation is 3.6 cm. Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform the t-test using the critical-value approach. A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 5% significance level, test the claim that the mean is less than 30 g.

Explanation / Answer

27. Yes, the given data is support to Z-test. Since population SD is given

H0: The mean is actually not lower than 560 F.

H1: The mean is actually lower than 560 F.

z Test
Test Statistic, z: -2.1724
Critical z: -2.3264
P-Value: 0.0149

Here Z value > Z critical value we do not reject H0

Thus conclud that the mean is actually not lower than 560 F.

28.

Yes, the given data is support to Z-test. Since population SD is given

H0: Population Mean is not greater than 50

H1: Population mean is greater than 50

z Test
Test Statistic, z: 1.8215
Critical z: 2.3264
P-Value: 0.0343

Here Z value < Z critical value, we accept H0

thus, we conclude that  Population Mean is not greater than 50

29)

Given sample size n = 16 which is <30 and also population SD is not given

So we have to use t-test.

H0: The population mean is not less than 30g

H1: The population mean is less than 30g

t Test
Test Statistic, t: -1.2727
Critical t: -1.7530
P-Value: 0.1112

Here t value > t critical value, we accept H0

Thus, we conclude that The population mean is not less than 30g

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.