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27 May, 06:23

On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?

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  1. 27 May, 08:32
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    The test statistic is - 2.5

    Yes, I can reject the null hypothesis at 5% significance level.

    Step-by-step explanation:

    Null hypothesis: The average number of sardines in a can is 9.75

    Alternate hypothesis: The average number of sardines in a can is greater than 9.75

    Test statistic (z) = (sample mean - population mean) : sd/√n

    sample mean = 9.75

    population mean = 10

    sd = 1

    n = 100

    z = (9.75 - 10) : 1/√100 = - 0.25 : 0.1 = - 2.5

    The test is a one-tailed test. At 5% significance level, the critical value is 1.645

    Conclusion:

    Reject the null hypothesis because the test statistic - 2.5 is less than the critical value 1.645
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