statistics 4.
posted by Steven on .
The manufacturer of Porshe 918 Spyder car claims that their car can go from 0 mph to 60 mph speed in less than 2.5 seconds. To test this claim, a sample of 40 new cars of this type were driven and their average 060 mph time was 2.6 seconds with a standard deviation of 0.5 seconds. Based on this information, would you believe the manufacturer’s claim? Use a 5% level of significance. State any assumptions you make. Clearly state the null and alternate hypotheses.
• A new television series must prove that it has more than 25% of the viewing audience after its initial 13week run in order to be judged successful. Assume that in a sample of 400 households, 112 were watching the series. At a 10% level of significance, can the series be judged successful based on this information? State any assumptions you make. Clearly state the null and alternate hypotheses.
• A bath soap manufacturing process is designed with the expectation that each batch prepared in the mixture department will produce a mean of 120 bars of soap per batch. A mean over or under this standard is undesirable. A sample of ten batches shows the following numbers of bars of soap:
108, 118, 120, 122, 119, 113, 124, 122, 120, 123
Use a 5% level of significance and test to see the null hypothesis H0: =120 should be rejected.
State any assumptions you make. Clearly state the alternate hypotheses

Here are a few ideas to get you started.
First problem:
Try a onesample ztest.
Formula:
z = (sample mean  population mean)/(standard deviation divided by the square root of sample size)
Your data:
sample mean = 2.6
population mean = 2.5
standard deviation = 0.5
sample size = 40
Plug values into the formula and calculate the ztest statistic.
Compare to the critical value for a onetailed test at .05 level of significance (you can determine this using a ztable). If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You will then be able to answer the question about the manufacturer's claim.
Second problem:
You can use a onesample proportional ztest for your data. (Test sample proportion = 112/400 or .28) Find the critical value in the appropriate table at .10 level of significance for a onetailed test. Compare the test statistic you calculate to the critical value from the table. If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You can draw your conclusions from there.
Third problem:
You will need to calculate mean and standard deviation for the data. Then use a onesample ttest or a onesample ztest. You can probably use the ttest since the sample size is small unless otherwise instructed.
I'll let you take it from here.