# Question

The Annual Survey of Hours and Earnings (ASHE) reports the weekly earnings of full time employees in various parts of Great Britain. In a recent survey, it was reported that average earnings in Cambridgeshire are “significantly higher” than the national average. To support this argument, it was noted that the Cambridgeshire sample had an average weekly income of £ 517, compared with the overall Great Britain average of £ 506 (source: Annual Survey of Hours and Earnings (ASHE), nomisweb. co. uk). If the Cambridgeshire sample consisted of 225 full time employees, set up a test to test a null hypothesis that the average Cambridgeshire income is no more than the national average (506), against an alternative hypothesis that the Cambridgeshire average is greater than the national average (506). Use a significance level of 5% and assume the Cambridgeshire population standard deviation is £ 75. Can we use the Cambridgeshire sample result to reject the null hypothesis?

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