Question

Need help with this testing a population proportion problem.

B A Response cats Hypothesis Test about a Population Proportion dogs cats =COUNTA(A2:A51) dogs Sample Size Response of Interest Count for Response Sample Proportion dogs cats =D5/D3 cats cats Hypothesized Value cats cats =SQRT(D8*(1-D8)/D3) Standard Error Test Statistic z cats dogs dogs dogs dogs =NORM.S.DIST(D11, TRUE) 14 p-value (Lower Tail) p-value (Upper Tail) p-value (Two Tail) 15 = 2*MIN(D13,014) Enter these same formulas in your downloaded Excel spreadsheet. Use the values produced by the proper formulas in your Excel sheet to conduct the following hypothesis test at a significance level of a = 0.01: Ho: p = 0.4 Ha: P = 0.4 The p-value is hypothesis and you than 40%. . Since this p-value is than a = 0.01, you reject the null conclude the percentage of students at the university who prefer dogs is different

Answer 1

Enter the following formula

A В с D Hypothesis Test about a Populatio 1 Response 2 cats 3 dogs Sample Size =COUNTA(A2:A51) 4 cats dogs Response of Interest 5 dogs Count for Response =COUNTIF(A2:A51,D4) 6 cats -D5/D3 Sample Proportion 7 cats 8 cats Hypothesized Value 0.4 9 cats SQRT (D8* (1-D8)/D3) 10 cats Standard Error 11 cats (D6-D8)/D10 Test Statistic z 12 dogs 13 dogs 14 dogs 15 dogs p-value (Lower Tail) p-value (Upper Tail) p-value (Two Tail) NORM.S.DIST(D11,TRU E) =1-NORM.S.DIST(D11,TRUE) =2*MIN(D13,D14)

get this (Note: Since only data for A2:A15 are provided, The results are based on those. You will get different values based on A2:A51. The formulas remain the same, but the conclusions could be different)

A B C D 1 Response Hypothesis Test about a Population Proportion 2 cats 3 dogs Sample Size 14 4 cats Response of Interest dogs 5 dogs Count for Response 6 cats Sample Proportion 0.4286 7 cats 8 cats Hypothesized Value 0.4 9 cats 10 cats Standard Error 0.1309 11 cats Test Statistic z 0.2182 12 dogs 13 dogs 14 dogs 15 dogs p-value (Lower Tail) p-value (Upper Tail) p-value (Two Tail) 0.5864 0.4136 0.8273 16

The hypotheses are

$\begin{align*} &H_0:p=0.4\leftarrow\text{null hypothesis}\\ &H_a:p\ne 0.4\leftarrow\text{alternative hypothesis}\\ \end{align*}$

This is a 2 tailed test (The alternative hypothesis has "not equal to"). We will reject the null hypothesis if the p-value is less than the significance level $\begin{align*} \alpha=0.01 \end{align*}$

Note: You will have a different p-value. Use that to conclude.

If the p-value is greater than 0.01 then use the following

ans: The p-value is 0.8273. Since the p-value is not less (or greater ) than  $\begin{align*} \alpha=0.01 \end{align*}$, you fail to reject the null hypothesis and you do not have sufficient evidence to conclude the percentage of students at the university who prefer dogs is different than 40%.

If the p-value is less than 0.01 (let us say it is 0.0018) then use the following

ans: The p-value is 0.0018. Since the p-value is less than  $\begin{align*} \alpha=0.01 \end{align*}$, you do reject the null hypothesis and you have sufficient evidence to conclude the percentage of students at the university who prefer dogs is different than 40%.