Question

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Test the claim that the proportion of people who own cats is smaller than 10% at the 0.005 significance level The null and alternative hypothesis would be: Ho:p 0.1 H0 : p> 0.1 Ho:p=0.1 H0'μ 0.1 Ha:p> 0.1 Hai p > 0.1 Ha: p < 0.1 HUP 0.1 Ho: μ-0.1 Ho: μ > 0.1 Ha : μ 0.1 Ha : μ < 0.1 The test is: right-tailed two-tailed left-tailed Based on a sample of 100 people, 6% owned cats The p-value is: (to 2 decimals) Based on this we: OReject the null hypothesis OFail to reject the null hypothesis

Answer 1

Answer

claim is that the proportion of people who own cats is less than 10%

So, for null hypothesis we assume that the proportion is equal to 10% and for alternate hypothesis, we assume that the proportion is less than 10%

we can write it as

So, option B is correct answer

Since the alternate hypothesis include less than symbol, so it is left tailed hypothesis.

Sample size is given as n = 100 and sample proportion = 6% / 6/100 = 0.06

population proportion = 10% = 10/100 = 0.10

Formula for test statistic is given as

setting the given values, we get

Now, we have to use z distribution to get the required p value. Look at -1.0 in left most column and 0.33 in the top most row.

we get

rounding to 2 decimals, we get p value = 0.09

At 0.005 level of significance, p value is greater than significance level, so result is insignificant.

We failed to reject the null hypothesis.