An article it was claimed that the typical supermarket trip takes a mean of 22 m

Question

An article it was claimed that the typical supermarket trip takes a mean of 22 minutes. In an effort to test this claim, you select a random sample of 50 shoppers. The mean shopping time for this sample was 25.36 minutes with a standard deviation of 7.24 minutes. Using the 0.1 level of significance, is there evidence that the mean shopping at this supermarket is different from the claimed value of 22 minutes?

A fast food chain has just developed a new process to make sure that orders at the drive-through are filled correctly. The previous process filled orders correctly 85% of the time. A sample of 100 orders using the new process is selected and 94 were filled correctly. At the 0.01 level of significance, can you conclude that the new process has increased the proportion of orders filled correctly?

Explanation / Answer

You need to set up hypotheses, calculate the z-test statistic (since this is a z-test), then compare to the critical value from a z-table to determine whether or not to reject the null hypothesis.

Hypotheses:

Ho: µ = 22 -->this is the null hypothesis.
Ha: µ does not equal 22 -->this is the alternate or alternative hypothesis.

This would be a two-tailed or nondirectional test because the alternative hypothesis doesn't specify a specific direction.

The reason we know this is a two-tailed test is because the problem asks if there is evidence that the mean time is different, which means the results could be in either tail of the distribution.

Therefore, using a z-test formula:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With your data:
z = (25.36 - 22)/(7.24/50)= 0.656

Now we will need to find the critical value at 0.10 level of significance using a z-table. Since this is a two-tailed test, we split the 0.10 into 0.05 and 0.05 for both tails of the distribution curve.

z=0.398 this is the critical value
since the observed value (calculated from a formula) exceeds our critical value we have to reject the null hypothesis and accept the alternative hypothesis

hence the mean shopping time at supermarket is different from the claimed 22 minutes.

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