Question

I need help determining the decision for null hypothesis. For 1&2, set the type one error to 1%

for 3-5, set the type one error to 5%

Go to Statcrunch shared data sets and use the file Nutritional Data for Fast Food 2017. Set the type one error equal to 1% Complete the following: 1) Use STAT - proportions stats - one sample w data to test the hypothesis that the proportion of "burgers" made by Wendy's restaurants is less than 0.18. set success = Wendy's. One sample proportion hypothesis test: Outcomes in : Fast Food Restaurant Success : Wendy's p: Proportion of successes Ho: p= 0.18 HA: p<0.18 Hypothesis test results: Variable Count Total Sample Prop. Std. Err. Z-Stat Fast Food Restaurant 12 126 0.095238095 0.034226139 -2.4765255 P-value 0.0066

Answer 1

The decision rule from P-value is:

If,P- value < level of Significance= $\alpha$ (i.e.type one error)

Then we reject H₀ (null hypothesis). And if,

P- value > level of Significance= $\alpha$ (i.e.type one error)

Then we do not reject H₀ (null hypothesis).

Given that, For 1&2, set the type one error to 1% i.e.$\alpha$ =0.01 level of Significance

Set 1) Decision: From hypothesis test result we observed that the P-value =0.0066

And .$\alpha$ =0.01 level of Significance

P-value < 0.01

Therefore we reject H₀ (null hypothesis) at 1% level of Significance.

Conclusion:

There is sufficient evidence to conclude that the proportion of "burgers" made by Wendy's restaurants is less than 0.18

Set 2) Decision: From hypothesis test result we observed that the P-value =0.8586

And .$\alpha$ =0.01 level of Significance

P-value > 0.01

Therefore we do not reject H₀ (null hypothesis) at 1% level of Significance.

Conclusion:

There is insufficient evidence to conclude that the proportion of "burgers" made by Wendy's restaurants is not equal to 0.10

Set 2) Decision: From hypothesis test result we observed that the P-value =0.8586

And .$\alpha$ =0.01 level of Significance

P-value > 0.01

Therefore we do not reject H₀ (null hypothesis) at 1% level of Significance.

Conclusion:

There is insufficient evidence to conclude that the proportion of "burgers" made by Wendy's restaurants is not equal to 0.10

For 3-5 data set type one error of 5%

Set 3) Decision: From hypothesis test result we observed that the P-value =< 0.0001

And $\alpha$ =0.05 level of Significance

P-value < 0.05

Therefore we reject H₀ (null hypothesis) at 5 % level of Significance.

Conclusion:

There is sufficient evidence to conclude that the population mean for calories is less than 700 calories.

Set 4) Decision: From hypothesis test result we observed that the P-value = 0.146

And $\alpha$ =0.05 level of Significance

P-value > 0.05

Therefore we do not reject H₀ (null hypothesis) at 5 % level of Significance.

Conclusion:

There is insufficient evidence to conclude that the population mean for calories is not equal to 500 calories.

Set 5) Decision: From hypothesis test result we observed that the P-value = 0.2872

And $\alpha$ =0.05 level of Significance

P-value > 0.05

Therefore we do not reject H₀ (null hypothesis) at 5 % level of Significance.

Conclusion:

There is insufficient evidence to conclude that the population mean for sodium is less than 1000 grams.