Question

A random sample of 10 scores on a recent chemistry exam is given below: 83818587797384867884 You may take as known that the population is normal with a standard deviation of 13. Carry out a hypothesis test (filling in the requested information) to determine if there is enough evidence at a 0.005 level of significance to infer that the mean score for this population exceeds 73.

Answer 1

Yes, we have enough evidence at a 0.005 level of significance to infer that the mean score for this population exceeds 73.

Explanation:

We are given that a random sample of 10 scores on a recent chemistry exam is given below:

83, 81, 85, 87, 79, 73, 84, 86, 78, 84

You may take as known that the population is normal with a standard deviation of 13.

We have to conduct a hypothesis test to infer that the mean score for this population exceeds 73.

Let
`\mu` = mean score for this population

SO, Null Hypothesis,
`H_0` :
`\mu \leq` 73 {means that the mean score for this population is less than or equal to 73}

Alternate Hypothesis,
`H_a` :
`\mu` > 73 {means that the mean score for this population exceeds 73}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean score =
`(83+81+85+87+79+73+84+86+78+84)/(10)` =
`(820)/(10)` = 82

`\sigma` = population standard deviation = 13

n = sample size = 10

So, test statistics =
`(82-73)/((13)/(√(10) ) )`

= 2.189

So, at 0.005 level of significance, the z table gives critical value of 3.8906 for one-tailed test. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean score for this population exceeds 73.